8 Answers
8

I have a good friend who says "Shalom Alecha" to me during kiddush levana. In fact this is the nusach brought in the by the Rama in the Shulchan Aruch (OC 426:2) and it's also in the Tur (OC 426). (Note that the Bach there comments that this is the proper version of the text.) I always smile and respond "Aleichem Shalom."

The greeting Shalom Alecha, in the singular form, appears in dozens of places in the Talmud.

I suspect that the usage of Sholom Aleichem stems from the famous song Friday night, where we are addressing multiple angels.

In addition, it is considered respectful to address elders using the plural form, and this usage may have become more commonplace since we usually use the words Shalom Aleichem when we are being a bit more formal.

I don't buy your explanation that it stems from the Shalom Aleichem prayer. The plural greeting is common all throughout the Middle East. Arabs say "As-Salamu Alaykum". Your second explanation seems to be correct though.
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Aaron ShaffierNov 30 '11 at 19:27

I heard in the name of the Hafes Haim (and it is brought down in Ben Yehoyada Berachot 3) that one has two angels that are with someone during the week, and two different ones that come on Shabbat (that's why we say Setechem LeShalom).

It could be, that the person who is greeting you is also greeting the angels.

@Vram I believe the Posekim say the reason why we don't say that prayer is because of "Yuhara" (i.e. only real Sadikim have angels with them). Therefor, it is some type of respect to the person when saying "alechem" because you are kinda saying they are a Sadik. I know, it sounds far fetched, but it's a try.
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Hacham GabrielFeb 20 '12 at 1:14

This is clearly as a show of respect. The second person plural can be used to show respect in Hebrew. Also in Arabic an almost identical greeting is universally used, "As-Salamu Alaykum". Seems pretty clear that this is something that goes back quite a long way in Middle Eastern culture including Judaism.

I once heard that at Kiddush Levana we say Shalom Aleichem - in plural - since we do not want to make the same error the moon made when it complained that 2 kings can not serve at the same time, therefore we say plural to include the moon and the sun. However this would not answer why when you meet a fellow on the street do we say it in plural.